The Yosef Lekach writes that Bigsan and Seresh’s being upset is described in the singular because they became one complete unit as partners in this Divinely-inspired, unnatural anger.
The Midrash (Esther Rabbah 6:13) says this anger is in the singular because it refers to H-Shem’s anger. He became angry at Achashverosh for the sake of the righteous Mordechai, whose wife was taken from him.
The gematria of Bigsan (2+3+400+50=455) is the exact gematria of “heimis” (“to kill”) (5+40+10+400=455), giving us indication that their goal was to assassinate the king, which was not otherwise explicit in the verse. Likewise, the gematria (and letters) of Seresh (400+300+200=900) is the same as reshes (“a net”) (200+300+400=900), which is a tool used to capture something before killing it. Similarly, as spelled in our verse, the word “v’Seresh” (“and Seresh”) (6+400+300+200=906) is equal to “mikshei maves” (“deadly traps”) (40+10+100+300+10+40+6+400=906).
Together, the gematria of the names Bigsan and Seresh (455+900=1355) equal the gematria of the phrase “Tiferes Mordechai” (“the glory of Mordechai”) (1081+274=1355). As we shall see in the next verse, Mordechai’s glory and abilities thwarted Bigsan and Seresh’s plot. Interestingly, the gematria of Seresh is almost exactly twice that of Bigsan.
Since the numbers divide almost equally into three parts, perhaps this hints to the Ibn Ezra’s opinion that there were three guards watching the king, but only these two were mentioned because of their plot.